steve, after further reasoning, I believe that what you say is another plausible explanation.
The sun orbits around the common center of mass of the binary system.
The orbit takes the sun closer and farther from another star. This star could be Sagittarius A* but might even be a closer star (a generic celestial object), which SY does not specify.
Such a Star, called the Vishnunabhi = the navel of Vishnu, is a celestial object which has the power to influence our earth an his inhabitants with spiritual enlightenment.
Even as the various planets carry an astrological influence upon the individual and the collective consciousness, Vishnunabhi, the misterious star, carries a powerful influence when the sun's orbit takes us closer to it.
Interestingly enough, Vishnunabhi might be a star pretty close to us, like Sirius, or Proxima Centauri (which are actually star systems themselves). This would make the sun's system very prone to its influence.
Sirius itself is a binary (or even ternary but not confirmed) system. If the sun's sytem rotates around Sirius, it would make it a quaternary system.
An X-ray image of Sirius A and Sirius B
